Gentle region: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-~~14 17~~:11:11 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-09 20:02:57 UTC</tt>.

: The original revision id was <tt>~~540983612~~</tt>.

: The original revision id was <tt>543524956</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Line 8:

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[Margo Schulter]], in a [[http://launch.groups.yahoo.com/group/tuning/message/38721|tuning list posting]], defined the "gentle region" of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later [[http://launch.groups.yahoo.com/group/tuning/message/105172|amending that]] to from 1.49 to 3.04 cents sharp. We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of [[29edo]], [[46edo]], [[75edo]], [[104edo]], [[109edo]], [[121edo]], [[145edo|133edo]], [[155edo]], [[162edo]], [[167edo]], [[179edo]], [[191edo]], [[201edo]], [[213edo]], [[225edo]] and [[237edo]], plus [[63edo]] and [[80edo]] in the extended region.

|| 17\29 || || || || || ~~703~~.~~448~~ || ||

|| 17\29 || || 703.448 || < 29 46 81| ||= 2\29

|| || || || || 61\104 || 703.846 || ||

82.759 ||= 3\29

|| || || || 44\75 || || ~~704~~ || ||

124.138 ||||= 6\29

|| || || || || 71\121 || 704.132 || ||

248.276 || ||

|| || || 27\46 || || || 704.348 || ||

|| || 61\104 || 703.846 || < 104 165 292| ||= 20\312

|| || || || || 118\201 || 704.478 || ||

76.923 ||= 33\208

|| || || || 91\155 || || ~~704~~.~~516~~ || ||

132.692 ||= 20\104

|| || || || || 155\264 || 704.5455 || ||

230.769 ||= 33\104

|| || 64\109 || || || || ~~704~~.~~587~~ || Boundary of smaller "gentle region" ||

265.385 || ||

|| || || || || ~~165~~\281 || ~~704~~.~~626~~ || ||

|| || 44\75 || 704 || < 75 119 211| ||= 14\225

|| || || || 101\172 || || 704.651 || ||

74.667 ||= 17\150

|| || || || || 138\235 || 704.681 || ||

136 ||= 14\75

|| || || || || || 704.~~7535~~ || ||

224 ||= 17\75

|| || || ~~37\63 || ||~~ || ~~704~~.~~762~~ || ||

272 || ||

|| || || || || |~~| 704~~.~~770~~ || ||

|| || 71\121 || 704.132 || < 121 192 340| ||= 23\363

|| || || || || 121\206 || 704.854 || ||

76.033 ||= 27\242

|| || || || 84\143 || || ~~704~~.~~895~~ || ||

133.884 ||= 23\121

|| || || || || 131\223 || 704.933 || ||

228.099 ||= 27\121

|| 47\80 || || || || || ~~705~~ || Boundary of larger "gentle region" ||</pre></div>

267.769 || ||

|| 27\46 || || 704.348 || < 46 73 129| ||= 3\46

78.261 ||= 5\46

130.435 ||= 9\46

234.783 ||= 10\46

260.87 || ||

|| || || 704.426 || < 29 46 81|+

< 109 173 306|

φ ||= 77.868 ||= 130.984 ||= 233.605 ||= 261.969 || ||

|| || 118\201 || 704.478 || < 201 319 564| ||= 13\201

77.612 ||= 22\201

131.343 ||= 39\201

232.836 ||= 44\201

262.687 || ||

|| || 91\155 || 704.516 || < 155 246 435| ||= 10\155

77.419 ||= 17\155

131.613 ||= 30\155

232.258 ||= 34\155

263.226 || ||

|| || 155\264 || 704.5455 || < 264 419 741| ||= 17\264

77.273 ||= 29\264

131.818 ||= 51\264

231.818 ||= 58\264

263.636 || ||

|| 64\109 || || 704.587 || < 109 173 306| ||= 7\109

77.064 ||= 12\109

132.11 ||= 21\109

231.192 ||= 24\109

264.22 || Boundary of smaller "gentle region" ||

|| || 165\281 || 704.626 || < 281 446 789| ||= 18\281

76.868 ||= 31\281

132.384 ||= 54\281

230.605 ||= 62\281

264.769 || ||

|| || 101\172 || 704.651 || < 172 273 483| ||= 11\172

76.744 ||= 19\172

132.558 ||= 33\172

230.232 ||= 38\172

265.116 || ||

|| || 138\235 || 704.681 || < 235 373 660| ||= 15\235

76.596 ||= 26\235

132.766 ||= 45\235

229.787 ||= 52\235

265.532 || ||

|| || || 704.716 || < 80 127 225|

+

< 109 173 306|

φ ||= 76.42 ||= 133.012 ||= 229.26 ||= 266.024 || ||

|| 37\63 || || 704.762 || < 63 100 177| ||= 4\63

76.1905 ||= 7\63

133.333 ||= 12\63

228.571 ||= 14\63

266.667 || ||

|| || 121\206 || 704.854 || < 206 327 578| ||= 40\618

77.67 ||= 45\412

131.068 ||= 40\206

233.01 ||= 45\206

262.136 || ||

|| || 84\143 || 704.895 || < 143 227 401| ||= 28\429

78.322 ||= 31\286

130.07 ||= 28\143

234.965 ||= 31\143

260.14 || ||

|| || 131\223 || 704.933 || < 223 354 626| ||= 43\669

77.13 ||= 49\446

131.839 ||= 43\223

231.39 ||= 49\223

263.667 || ||

|| 47\80 || || 705 || < 80 127 225| ||= 5\80

75 ||= 9\80

135 ||= 15\80

225 ||= 18\80

270 || Boundary of larger "gentle region" ||</pre></div>

<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gentle region</title></head><body><a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a>, in a <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/38721" rel="nofollow">tuning list posting</a>, defined the &quot;gentle region&quot; of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/105172" rel="nofollow">amending that</a> to from 1.49 to 3.04 cents sharp. We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of <a class="wiki_link" href="/29edo">29edo</a>, <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/75edo">75edo</a>, <a class="wiki_link" href="/104edo">104edo</a>, <a class="wiki_link" href="/109edo">109edo</a>, <a class="wiki_link" href="/121edo">121edo</a>, <a class="wiki_link" href="/145edo">133edo</a>, <a class="wiki_link" href="/155edo">155edo</a>, <a class="wiki_link" href="/162edo">162edo</a>, <a class="wiki_link" href="/167edo">167edo</a>, <a class="wiki_link" href="/179edo">179edo</a>, <a class="wiki_link" href="/191edo">191edo</a>, <a class="wiki_link" href="/201edo">201edo</a>, <a class="wiki_link" href="/213edo">213edo</a>, <a class="wiki_link" href="/225edo">225edo</a> and <a class="wiki_link" href="/237edo">237edo</a>, plus <a class="wiki_link" href="/63edo">63edo</a> and <a class="wiki_link" href="/80edo">80edo</a> in the extended region.

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<td>

</td>

<td>

<td>703.448

</td>

<td>&lt; 29 46 81|

</td>

<td>

<td style="text-align: center;">2\29

82.759

</td>

<td>

<td style="text-align: center;">3\29

124.138

</td>

<td>~~703~~.~~448~~

<td colspan="2" style="text-align: center;">6\29

248.276

</td>

<td>

Line 52:

Line 129:

<td>

</td>

<td>

<td>61\104

</td>

<td>703.846

</td>

<td>&lt; 104 165 292|

</td>

<td>

<td style="text-align: center;">20\312

76.923

</td>

<td>

<td style="text-align: center;">33\208

132.692

</td>

<td>61\104

<td style="text-align: center;">20\104

230.769

</td>

<td>~~703~~.~~846~~

<td style="text-align: center;">33\104

265.385

</td>

<td>

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<td>

</td>

<td>

<td>44\75

</td>

<td>704

</td>

<td>&lt; 75 119 211|

</td>

<td>

<td style="text-align: center;">14\225

74.667

</td>

<td>44\75

<td style="text-align: center;">17\150

136

</td>

<td>

<td style="text-align: center;">14\75

224

</td>

<td>~~704~~

<td style="text-align: center;">17\75

272

</td>

<td>

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<td>

</td>

<td>

<td>71\121

</td>

<td>704.132

</td>

<td>&lt; 121 192 340|

</td>

<td>

<td style="text-align: center;">23\363

76.033

</td>

<td>

<td style="text-align: center;">27\242

133.884

</td>

<td>71\121

<td style="text-align: center;">23\121

228.099

</td>

<td>~~704~~.~~132~~

<td style="text-align: center;">27\121

267.769

</td>

<td>

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</tr>

<tr>

<td>27\46

</td>

<td>

</td>

<td>

<td>704.348

</td>

<td>&lt; 46 73 129|

</td>

<td>27\46

<td style="text-align: center;">3\46

78.261

</td>

<td>

<td style="text-align: center;">5\46

130.435

</td>

<td>

<td style="text-align: center;">9\46

234.783

</td>

<td>~~704~~.~~348~~

<td style="text-align: center;">10\46

260.87

</td>

<td>

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<td>

</td>

<td>

<td>704.426

</td>

<td>&lt; 29 46 81|+

&lt; 109 173 306|

φ

</td>

<td style="text-align: center;">77.868

</td>

<td>

<td style="text-align: center;">130.984

</td>

<td>~~118\201~~

<td style="text-align: center;">233.605

</td>

<td>~~704~~.~~478~~

<td style="text-align: center;">261.969

</td>

<td>

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<td>

</td>

<td>

<td>118\201

</td>

<td>704.478

</td>

<td>&lt; 201 319 564|

</td>

<td>

<td style="text-align: center;">13\201

77.612

</td>

<td>91\~~155~~

<td style="text-align: center;">22\201

131.343

</td>

<td>

<td style="text-align: center;">39\201

232.836

</td>

<td>~~704~~.~~516~~

<td style="text-align: center;">44\201

262.687

</td>

<td>

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<td>

</td>

<td>

<td>91\155

</td>

<td>704.516

</td>

<td>&lt; 155 246 435|

</td>

<td>

<td style="text-align: center;">10\155

77.419

</td>

<td>

<td style="text-align: center;">17\155

131.613

</td>

<td>155~~\264~~

<td style="text-align: center;">30\155

232.258

</td>

<td>~~704~~.~~5455~~

<td style="text-align: center;">34\155

263.226

</td>

<td>

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<td>

</td>

<td>64\~~109~~

<td>155\264

</td>

<td>704.5455

</td>

<td>&lt; 264 419 741|

</td>

<td>

<td style="text-align: center;">17\264

77.273

</td>

<td>

<td style="text-align: center;">29\264

131.818

</td>

<td>

<td style="text-align: center;">51\264

231.818

</td>

<td>~~704~~.~~587~~

<td style="text-align: center;">58\264

263.636

</td>

<td&gt~~;Boundary of smaller &quot;gentle region&quot~~;

<td>

</td>

</tr>

<tr>

<td>64\109

</td>

<td>

</td>

<td>

<td>704.587

</td>

<td>&lt; 109 173 306|

</td>

<td>

<td style="text-align: center;">7\109

77.064

</td>

<td>

<td style="text-align: center;">12\109

132.11

</td>

<td>~~165~~\~~281~~

<td style="text-align: center;">21\109

231.192

</td>

<td>~~704~~.~~626~~

<td style="text-align: center;">24\109

264.22

</td>

<td>

<td>Boundary of smaller &quot;gentle region&quot;

</td>

</tr>

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<td>

</td>

<td>

<td>165\281

</td>

<td>704.626

</td>

<td>&lt; 281 446 789|

</td>

<td>

<td style="text-align: center;">18\281

76.868

</td>

<td>~~101~~\~~172~~

<td style="text-align: center;">31\281

132.384

</td>

<td>

<td style="text-align: center;">54\281

230.605

</td>

<td>~~704~~.~~651~~

<td style="text-align: center;">62\281

264.769

</td>

<td>

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<td>

</td>

<td>

<td>101\172

</td>

<td>704.651

</td>

<td>&lt; 172 273 483|

</td>

<td>

<td style="text-align: center;">11\172

76.744

</td>

<td>

<td style="text-align: center;">19\172

132.558

</td>

<td>~~138~~\~~235~~

<td style="text-align: center;">33\172

230.232

</td>

<td>~~704~~.~~681~~

<td style="text-align: center;">38\172

265.116

</td>

<td>

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<td>

</td>

<td>

<td>138\235

</td>

<td>704.681

</td>

<td>&lt; 235 373 660|

</td>

<td>

<td style="text-align: center;">15\235

76.596

</td>

<td>

<td style="text-align: center;">26\235

132.766

</td>

<td>

<td style="text-align: center;">45\235

229.787

</td>

<td>~~704~~.~~7535~~

<td style="text-align: center;">52\235

265.532

</td>

<td>

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<td>

</td>

<td>~~37\63~~

<td>704.716

</td>

<td>&lt; 80 127 225|

+

&lt; 109 173 306|

φ

</td>

<td style="text-align: center;">76.42

</td>

<td>

<td style="text-align: center;">133.012

</td>

<td>

<td style="text-align: center;">229.26

</td>

<td>~~704~~.~~762~~

<td style="text-align: center;">266.024

</td>

<td>

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</tr>

<tr>

<td>37\63

</td>

<td>

</td>

<td>

<td>704.762

</td>

<td>&lt; 63 100 177|

</td>

<td>

<td style="text-align: center;">4\63

76.1905

</td>

<td>

<td style="text-align: center;">7\63

133.333

</td>

<td>

<td style="text-align: center;">12\63

228.571

</td>

<td>~~704~~.~~770~~

<td style="text-align: center;">14\63

266.667

</td>

<td>

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<td>

</td>

<td>

<td>121\206

</td>

<td>704.854

</td>

<td>&lt; 206 327 578|

</td>

<td>

<td style="text-align: center;">40\618

77.67

</td>

<td>

<td style="text-align: center;">45\412

131.068

</td>

<td>~~121~~\206

<td style="text-align: center;">40\206

233.01

</td>

<td>~~704~~.~~854~~

<td style="text-align: center;">45\206

262.136

</td>

<td>

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<td>

</td>

<td>

<td>84\143

</td>

<td>704.895

</td>

<td>&lt; 143 227 401|

</td>

<td>

<td style="text-align: center;">28\429

78.322

</td>

<td>84\~~143~~

<td style="text-align: center;">31\286

130.07

</td>

<td>

<td style="text-align: center;">28\143

234.965

</td>

<td>~~704~~.~~895~~

<td style="text-align: center;">31\143

260.14

</td>

<td>

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<td>

</td>

<td>

<td>131\223

</td>

<td>704.933

</td>

<td>&lt; 223 354 626|

</td>

<td>

<td style="text-align: center;">43\669

77.13

</td>

<td>

<td style="text-align: center;">49\446

131.839

</td>

<td>~~131~~\223

<td style="text-align: center;">43\223

231.39

</td>

<td>~~704~~.~~933~~

<td style="text-align: center;">49\223

263.667

</td>

<td>

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<td>

</td>

<td>

<td>705

</td>

<td>&lt; 80 127 225|

</td>

<td style="text-align: center;">5\80

75

</td>

<td>

<td style="text-align: center;">9\80

135

</td>

<td>

<td style="text-align: center;">15\80

225

</td>

<td>~~705~~

<td style="text-align: center;">18\80

270

</td>

<td>Boundary of larger &quot;gentle region&quot;

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-14 17:11:11 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-09 20:02:57 UTC</tt>.<br>
-: The original revision id was <tt>540983612</tt>.<br>
+: The original revision id was <tt>543524956</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 8: / Line 8: @@
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[Margo Schulter]], in a [[http://launch.groups.yahoo.com/group/tuning/message/38721|tuning list posting]], defined the "gentle region" of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later [[http://launch.groups.yahoo.com/group/tuning/message/105172|amending that]] to from 1.49 to 3.04 cents sharp. We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of [[29edo]], [[46edo]], [[75edo]], [[104edo]], [[109edo]], [[121edo]], [[145edo|133edo]], [[155edo]], [[162edo]], [[167edo]], [[179edo]], [[191edo]], [[201edo]], [[213edo]], [[225edo]] and [[237edo]], plus [[63edo]] and [[80edo]] in the extended region.
-|| 17\29 ||   ||   ||   ||   || 703.448 ||   ||
+|| 17\29 ||   || 703.448 || &lt; 29 46 81| ||= 2\29
-||   ||   ||   ||   || 61\104 || 703.846 ||   ||
+.759 ||= 3\29
-||   ||   ||   || 44\75 ||   || 704 ||   ||
+.138 ||||= 6\29
-||   ||   ||   ||   || 71\121 || 704.132 ||   ||
+.276 ||   ||
-||   ||   || 27\46 ||   ||   || 704.348 ||   ||
+||   || 61\104 || 703.846 || &lt; 104 165 292| ||= 20\312
-||   ||   ||   ||   || 118\201 || 704.478 ||   ||
+.923 ||= 33\208
-||   ||   ||   || 91\155 ||   || 704.516 ||   ||
+.692 ||= 20\104
-||   ||   ||   ||   || 155\264 || 704.5455 ||   ||
+.769 ||= 33\104
-||   || 64\109 ||   ||   ||   || 704.587 || Boundary of smaller "gentle region" ||
+.385 ||   ||
-||   ||   ||   ||   || 165\281 || 704.626 ||   ||
+||   || 44\75 || 704 || &lt; 75 119 211| ||= 14\225
-||   ||   ||   || 101\172 ||   || 704.651 ||   ||
+.667 ||= 17\150
-||   ||   ||   ||   || 138\235 || 704.681 ||   ||
+||= 14\75
-||   ||   ||   ||   ||   || 704.7535 ||   ||
+||= 17\75
-||   ||   || 37\63 ||   ||   || 704.762 ||   ||
+||   ||
-||   ||   ||   ||   ||   || 704.770 ||   ||
+||   || 71\121 || 704.132 || &lt; 121 192 340| ||= 23\363
-||   ||   ||   ||   || 121\206 || 704.854 ||   ||
+.033 ||= 27\242
-||   ||   ||   || 84\143 ||   || 704.895 ||   ||
+.884 ||= 23\121
-||   ||   ||   ||   || 131\223 || 704.933 ||   ||
+.099 ||= 27\121
-|| 47\80 ||   ||   ||   ||   || 705 || Boundary of larger "gentle region" ||</pre></div>
+.769 ||   ||
+|| 27\46 ||   || 704.348 || &lt; 46 73 129| ||= 3\46
+.261 ||= 5\46
+.435 ||= 9\46
+.783 ||= 10\46
+.87 ||   ||
+||   ||   || 704.426 || &lt; 29 46 81|+
+&lt; 109 173 306|
+&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||= 77.868 ||= 130.984 ||= 233.605 ||= 261.969 ||   ||
+||   || 118\201 || 704.478 || &lt; 201 319 564| ||= 13\201
+.612 ||= 22\201
+.343 ||= 39\201
+.836 ||= 44\201
+.687 ||   ||
+||   || 91\155 || 704.516 || &lt; 155 246 435| ||= 10\155
+.419 ||= 17\155
+.613 ||= 30\155
+.258 ||= 34\155
+.226 ||   ||
+||   || 155\264 || 704.5455 || &lt; 264 419 741| ||= 17\264
+.273 ||= 29\264
+.818 ||= 51\264
+.818 ||= 58\264
+.636 ||   ||
+|| 64\109 ||   || 704.587 || &lt; 109 173 306| ||= 7\109
+.064 ||= 12\109
+.11 ||= 21\109
+.192 ||= 24\109
+.22 || Boundary of smaller "gentle region" ||
+||   || 165\281 || 704.626 || &lt; 281 446 789| ||= 18\281
+.868 ||= 31\281
+.384 ||= 54\281
+.605 ||= 62\281
+.769 ||   ||
+||   || 101\172 || 704.651 || &lt; 172 273 483| ||= 11\172
+.744 ||= 19\172
+.558 ||= 33\172
+.232 ||= 38\172
+.116 ||   ||
+||   || 138\235 || 704.681 || &lt; 235 373 660| ||= 15\235
+.596 ||= 26\235
+.766 ||= 45\235
+.787 ||= 52\235
+.532 ||   ||
+||   ||   || 704.716 || &lt; 80 127 225|
++
+&lt; 109 173 306|
+&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||= 76.42 ||= 133.012 ||= 229.26 ||= 266.024 ||   ||
+|| 37\63 ||   || 704.762 || &lt; 63 100 177| ||= 4\63
+.1905 ||= 7\63
+.333 ||= 12\63
+.571 ||= 14\63
+.667 ||   ||
+||   || 121\206 || 704.854 || &lt; 206 327 578| ||= 40\618
+.67 ||= 45\412
+.068 ||= 40\206
+.01 ||= 45\206
+.136 ||   ||
+||   || 84\143 || 704.895 || &lt; 143 227 401| ||= 28\429
+.322 ||= 31\286
+.07 ||= 28\143
+.965 ||= 31\143
+.14 ||   ||
+||   || 131\223 || 704.933 || &lt; 223 354 626| ||= 43\669
+.13 ||= 49\446
+.839 ||= 43\223
+.39 ||= 49\223
+.667 ||   ||
+|| 47\80 ||   || 705 || &lt; 80 127 225| ||= 5\80
+||= 9\80
+||= 15\80
+||= 18\80
+|| Boundary of larger "gentle region" ||</pre></div>
 <h4>Original HTML content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Gentle region&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link" href="/Margo%20Schulter"&gt;Margo Schulter&lt;/a&gt;, in a &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/38721" rel="nofollow"&gt;tuning list posting&lt;/a&gt;, defined the &amp;quot;gentle region&amp;quot; of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/105172" rel="nofollow"&gt;amending that&lt;/a&gt; to from 1.49 to 3.04 cents sharp. We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;, &lt;a class="wiki_link" href="/75edo"&gt;75edo&lt;/a&gt;, &lt;a class="wiki_link" href="/104edo"&gt;104edo&lt;/a&gt;, &lt;a class="wiki_link" href="/109edo"&gt;109edo&lt;/a&gt;, &lt;a class="wiki_link" href="/121edo"&gt;121edo&lt;/a&gt;, &lt;a class="wiki_link" href="/145edo"&gt;133edo&lt;/a&gt;, &lt;a class="wiki_link" href="/155edo"&gt;155edo&lt;/a&gt;, &lt;a class="wiki_link" href="/162edo"&gt;162edo&lt;/a&gt;, &lt;a class="wiki_link" href="/167edo"&gt;167edo&lt;/a&gt;, &lt;a class="wiki_link" href="/179edo"&gt;179edo&lt;/a&gt;, &lt;a class="wiki_link" href="/191edo"&gt;191edo&lt;/a&gt;, &lt;a class="wiki_link" href="/201edo"&gt;201edo&lt;/a&gt;, &lt;a class="wiki_link" href="/213edo"&gt;213edo&lt;/a&gt;, &lt;a class="wiki_link" href="/225edo"&gt;225edo&lt;/a&gt; and &lt;a class="wiki_link" href="/237edo"&gt;237edo&lt;/a&gt;, plus &lt;a class="wiki_link" href="/63edo"&gt;63edo&lt;/a&gt; and &lt;a class="wiki_link" href="/80edo"&gt;80edo&lt;/a&gt; in the extended region.&lt;br /&gt;
@@ Line 38: / Line 110: @@
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+        &lt;td&gt;703.846&lt;br /&gt;
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+        &lt;td&gt;&amp;lt; 104 165 292|&lt;br /&gt;
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-         &lt;td&gt;704&lt;br /&gt;
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-         &lt;td&gt;704.132&lt;br /&gt;
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@@ Line 98: / Line 199: @@
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+        &lt;td&gt;&amp;lt; 46 73 129|&lt;br /&gt;
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-         &lt;td&gt;&lt;br /&gt;
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+&lt;/td&gt;
+        &lt;td&gt;&amp;lt; 29 46 81|+&lt;br /&gt;
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+&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
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-         &lt;td&gt;704.478&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;261.969&lt;br /&gt;
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@@ Line 132: / Line 247: @@
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@@ Line 164: / Line 295: @@
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+        &lt;td&gt;&amp;lt; 264 419 741|&lt;br /&gt;
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-         &lt;td&gt;Boundary of smaller &amp;quot;gentle region&amp;quot;&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
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-         &lt;td&gt;&lt;br /&gt;
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@@ Line 196: / Line 343: @@
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@@ Line 212: / Line 367: @@
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@@ Line 228: / Line 391: @@
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@@ Line 246: / Line 417: @@
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-         &lt;td&gt;37\63&lt;br /&gt;
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+&lt;/td&gt;
+        &lt;td&gt;&amp;lt; 80 127 225|&lt;br /&gt;
++&lt;br /&gt;
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-         &lt;td&gt;704.762&lt;br /&gt;
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@@ Line 258: / Line 436: @@
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-         &lt;td&gt;&lt;br /&gt;
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@@ Line 276: / Line 462: @@
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-         &lt;td&gt;&lt;br /&gt;
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@@ Line 292: / Line 486: @@
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-         &lt;td&gt;&lt;br /&gt;
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@@ Line 308: / Line 510: @@
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-         &lt;td&gt;&lt;br /&gt;
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+&lt;br /&gt;
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          &lt;td&gt;Boundary of larger &amp;quot;gentle region&amp;quot;&lt;br /&gt;